Being religious does not mean being orthodox. And even among orthodox religious people there’s a lot of variability in beliefs. Religious people are absolutely welcome in LGBT communities, given that they aren’t bigoted towards queer people. If you are queer positive and support queer rights, then it doesn’t matter what your religious beliefs are. Lots of queer people are religious as well. Queer spaces are for them too.
Christian Anarchy specifically has a long history dating in some ways back to the early church period. A very direct interpretation of the New Testament clearly directs one to renounce wealth inequality and to view all people as equals. Especially the beatitudes from the sermon on the mount, which literally says that the poor and persecuted are blessed and will be the ones to go to heaven. Many Christian anarchists view the violence of the state as inherently incompatible with Jesus’s command in the antithesis “to love thy enemy” and “turn the other cheek.” It is also commonly argued that nationalism is an example of idolatry, which is condemned in the ten commandments.
Jesus himself lived what can only be described as a bohemian lifestyle. He ejected the merchants from the second temple. He criticized kings and merchants. He was a willing martyr, willing to die rather than to resist violently.
All these things contribute to the long-standing traditions of Christian Anarchy. A very literal interpretation of his teachings and emulation of his way of life leads one pretty naturally to anarchy. There exist anarchist communities in many major religions.